Document 1: Memo from Apple Orchard Owners to Employees
Our apple orchard is proud to have one of the most productive fields of pink lady apples in the area. Nonetheless, to stay
ahead of our competitors, we are considering instituting a new system of misting pumps designed to spray water over the
field during dry spells. We must now decide whether these misting pumps will make a profitable increase in productivity
To cover the entire field, we would need 100 pumps. Our field has been divided into 100 plots, as shown with the
numbering system below, where the 100th plot is marked as 00. We have purchased only 10 misting pumps for this year
for our trial run.
The chart below (with boldface numbers) shows the number of bushels of apples harvested last year from each plot.
Generally, productivity tends to be higher on the south (bottom) side of the field because of proximity to the water from
the Maple Creek riverbed.
The total harvested from last year was 3,631 bushels.
We are seeking input from all of our employees about which of the 10 plots of land are best suited for placing our 10
misting pumps to get a good representation of their effect on productivity this year.
Document 2: Pump Placement Proposal from Employee A
I recommend that we place the pumps randomly throughout the field. We could use a list of randomly generated digits
from a computer, as listed below, and select the first 10 plots that are identified. As an example, plot number 83 would
be first plot chosen. Each plot will receive a misting pump, and then we will check on the increase in productivity,
comparing this year to last year. Any gains we find should be multiplied by 10 to estimate the increase in productivity
of the whole field.
Random digits: 8305862487062637354832412
Document 3: Pump Placement Proposal from Employee B
I recommend that we place all 10 pumps on the east (right) side of the field, to cover plots 10, 20, 30, etc., up to 00. The
reason is that this way, every east-west row of the field is represented with one misting pump. Any gains we find should
be multiplied by 10 to estimate the increase in productivity of the whole field.
Consider each of the following statements. Does the information in the three sources support the inference as stated?
If Employee A’s program had been implemented, using consecutive two digit pairs of numbers to represent individual plots, the total number of bushels produced on those 10 plots, when multiplied by 10, would underestimate the total productivity of the entire field.
Since Employee A is using computer generated randomized digits, his plan will be successful in representing the entire field since there is no human bias in the selection, unlike Employee B.
If Employee B had suggested all ten plots at the west (left) end of the field, his computations for productivity would have been roughly the same (within a 5% error) as the computation resulting from his suggestion about using all ten plots on the east (right) end of the field.
If Employee B had decided to simply choose one plot from every east-west row, independent of the other rows, and if Employee A had chosen 10 plots at random from anywhere in the field, then the lowest and highest possible estimates from Employee B would differ by less than the lowest and highest possible estimates from Employee A.